Exact multi-soliton solutions in the four dimensional Skyrme model

TL;DR

This paper presents exact multi-soliton solutions in a four-dimensional Skyrme model on a finite volume, revealing new topological properties and matching experimental data for nucleon masses.

Contribution

It introduces exact multi-Skyrmion solutions with an additional topological charge and a novel BPS bound in a finite volume Skyrme model.

Findings

Exact multi-Skyrmion solutions with arbitrary winding number.

A new BPS bound that can be saturated.

Model parameters agree with experimental nucleon data.

Abstract

Exact analytic solutions of the Skyrme model defined on a spherically symmetric $R^{(1,1)} \times S^2$ geometry, chosen to mimic finite volume effects, are presented. The static and spherically symmetric configurations have non-trivial winding number and finite soliton mass. These configurations possess an extra topological charge, allowing for a novel BPS bound which can be saturated, unlike what happens in the standard case. Such solutions include exact multi-Skyrmions of arbitrary winding number, composed by interacting elementary Skyrmions. The values of the coupling constants and the compression modulus are found in good agreement with experiments by fitting the masses $M_N$ and $M_\Delta$.